$$S(t)=Pr(T > t), t\in (0,\infty)$$
$$S(t) \ge 0, \forall t \in \mathbb{R}^{+}$$
$$\begin{aligned}S(0)&=1\\\\ \displaystyle\lim_{t \to \infty} S(t)&=0\end{aligned}$$
Alternate names
The reliability function
The complementary cumulative distribution function
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